Subgroups — #21445949

Order 7808.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#92418	C₂	1	1	yes	maximal, characteristic
2	#16839628	C₂	1	1	yes	maximal, characteristic
3	#16839524	C₂	1	4	yes	maximal
4	C₆₁×#382	C₂	1	1	yes	maximal, characteristic
5	C₂²×#92418	C₂²	1	2	yes	—
6	C₂×C₄⋊Dic₆₁	C₂²	1	2	yes	—
7	C₄×#92418	C₄	1	4	yes	complemented
8	#14519684	—	2	2	no	—
9	C₂×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
10	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
11	#95×C₆₁	—	2	2	no	—
12	C₂²×C₄×C₆₁	—	2	2	no	—
13	C₂²×C₄×C₆₁	D₄	1	2	yes	—
14	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
15	C₂²×Dic₆₁	—	2	2	no	—
16	C₄⋊C₄×C₆₁	—	2	4	no	—
17	C₄²×C₆₁	C₂×C₄	1	2	yes	—
18	C₄²×C₆₁	Q₈	1	2	yes	—
19	C₄⋊Dic₆₁	—	2	4	no	—
20	C₂×#92418	—	2	2	no	—
21	C₂×#92418	—	2	2	no	—
22	C₂×#92418	C₂×C₄	1	4	yes	—
23	C₂³×C₆₁	C₂×D₄	1	1	yes	characteristic
24	C₂×C₄×C₆₁	—	2	4	no	—
25	C₂×C₄×C₆₁	—	4	2	no	—
26	C₂×C₄×C₆₁	—	4	4	no	—
27	C₂×C₄×C₆₁	C₄⋊C₄	1	4	yes	—
28	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₄×C₆₁	#41	1	2	yes	—
31	C₂×C₄×C₆₁	#41	1	2	yes	—
32	C₂×Dic₆₁	—	4	2	no	—
33	C₂×Dic₆₁	—	4	4	no	—
34	#92418	—	2	4	no	—
35	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂²×C₆₁	#124	1	1	yes	characteristic
37	C₂²×C₆₁	#124	1	1	yes	characteristic
38	C₂²×C₆₁	#135	1	4	yes	—
39	C₄×C₆₁	—	2	4	no	—
40	C₄×C₆₁	—	8	2	no	—
41	C₄×C₆₁	#117	1	2	yes	—
42	C₄×C₆₁	#125	1	2	yes	—
43	Dic₆₁	—	8	2	no	—
44	#1835	—	61	1	no	maximal, Sylow
45	C₂×C₆₁	#382	1	1	yes	characteristic
46	C₂×C₆₁	#427	1	2	yes	—
47	C₂×C₆₁	#488	1	2	yes	—
48	C₂×C₆₁	#488	1	2	yes	—
49	C₂×C₄×C₈	—	61	1	no	—
50	#382	—	61	1	no	—
51	#382	D₆₁	1	1	yes	characteristic
52	#340	—	61	4	no	—
53	C₆₁	#1835	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₈	—	61	2	no	—
55	C₂×C₄⋊C₄	—	61	2	no	—
56	C₂×C₄⋊C₄	C₂×D₆₁	1	2	yes	—
57	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
58	C₄×C₈	—	61	4	no	—
59	#95	—	2	2	no	—
60	#95	—	122	2	no	—
61	C₂²×C₄	—	2	2	no	—
62	C₂²×C₄	—	122	2	no	—
63	C₂²×C₄	C₂²⋊D₆₁	1	2	yes	—
64	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
65	C₂×C₈	—	61	4	no	—
66	C₂×C₈	—	122	2	no	—
67	C₂×C₈	—	122	2	no	—
68	C₄⋊C₄	—	2	4	no	—
69	C₄⋊C₄	—	122	4	no	—
70	C₄²	Dic₁₂₂	1	2	yes	—
71	C₄²	C₄×D₆₁	1	2	yes	—
72	C₂³	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
73	C₂×C₄	—	2	4	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	4	4	no	—
76	C₂×C₄	—	244	2	no	—
77	C₂×C₄	—	244	4	no	—
78	C₂×C₄	#11758196	1	4	yes	—
79	C₂×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
80	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
81	C₂×C₄	#11758224	1	2	yes	—
82	C₂×C₄	#11758226	1	2	yes	—
83	C₈	—	122	4	no	—
84	C₂²	C₂×#11758196	1	1	yes	characteristic
85	C₂²	#14519764	1	1	yes	characteristic
86	C₂²	#14519766	1	1	yes	characteristic
87	C₂²	#14519797	1	4	yes	—
88	C₄	—	2	4	no	—
89	C₄	—	8	2	no	—
90	C₄	—	488	2	no	—
91	C₄	#14519735	1	2	yes	—
92	C₄	#14519768	1	2	yes	—
93	C₂	#16839627	1	1	yes	characteristic
94	C₂	#16839798	1	2	yes	—
95	C₂	#16840116	1	2	yes	—
96	C₂	#16840119	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₆₁
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₆₁×#382	C₂
socle	C₂³×C₆₁	C₂×D₄
hypercenter	#382	D₆₁
hypocenter	C₆₁	#1835
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
7. C₄×#92418	C₄	semidirect
53. C₆₁	#1835	semidirect